Mobile's Initial Position: Solving S(t) = 10 + 3.5t

Hey everyone! Let's dive into this physics problem where we're given a time-based function, S(t) = 10 + 3.5t, and we need to figure out where the mobile (or object) is located at the origin of time. It sounds a bit complex, but trust me, it's simpler than it looks! We'll break it down step by step, making sure everyone understands the fundamentals and logic behind the solution. Think of it as a fun brain workout rather than a daunting task. So, let's put on our thinking caps and get started!

Understanding the Time Function

First off, let’s really understand what this time function is telling us. In the equation S(t) = 10 + 3.5t, S(t) represents the position of the mobile at a given time 't'. The '10' is a constant—it's the initial position of the mobile when time t is zero. The '3.5' is the velocity, indicating how much the position changes for each unit of time that passes. The 't' is, of course, the time. So, what we're seeing here is a linear equation, which means the mobile is moving at a constant speed in a straight line. This kind of motion is known as uniform motion, and it's one of the most basic concepts in physics. Now, let's zoom in on the question: “Where is the mobile at the origin of times?” This is just another way of asking, “What is the position of the mobile when time (t) equals zero?” Understanding the question is half the battle, guys. Once you grasp what’s being asked, the path to the solution becomes much clearer. So, with this basic understanding in place, we can proceed to the next step: plugging in the numbers and crunching them to find our answer. Keep the momentum going!

Solving for the Initial Position

Okay, so now we know the question is essentially asking us to find the position, S(t), when time, 't', is zero. This is super straightforward! To find the initial position, all we need to do is plug '0' into our equation wherever we see 't'. So, our equation S(t) = 10 + 3.5t becomes S(0) = 10 + 3.5 * (0). Remember, any number multiplied by zero is zero, right? So, 3.5 multiplied by 0 is simply 0. Now our equation looks like this: S(0) = 10 + 0. And what’s 10 plus 0? It’s 10, of course! So, S(0) = 10. What does this tell us? It tells us that the position of the mobile at time zero is 10. In other words, at the very beginning, when time hadn't started ticking yet, the mobile was located at the 10-meter mark. See? It’s like a piece of cake when you break it down step by step. This is a classic example of how understanding basic algebraic principles can help us solve physics problems. The key here is to substitute the given value into the equation and then simplify. It’s like following a recipe: put in the right ingredients, follow the steps, and you get the perfect result! Let’s keep going; we're on a roll here!

Identifying the Correct Answer

Alright, so we've done the math and found that S(0) equals 10. This means that at the origin of times (when t = 0), the mobile is located at 10 meters. Now, we need to match this result with the options provided in the question. Let's quickly recap the options: a. 0 m, b. 3.5 m, c. Nenhuma das alternativas (which means